Nonclassicality of optical fields is helpful in understanding fundamentals
of quantum optics and have many applications in quantum information
processing [1]}. To generate and manipulate various nonclassical optical
fields, subtracting or adding photons from/to traditional quantum states or
Gaussian states is proposed [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}. For example, the photon
addition and subtraction have been successfully demonstrated experimentally
for probing quantum commutation rules by Parigi et al. [7]}.
Recently, photon-added (-subtracted) Gaussian states have received more
attention from both experimentalists and theoreticians [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, since these states exhibit an abundant of
nonclassical properties and may give access to a complete engineering of
quantum states and to fundamental quantum phenomena.
